Finite Group DatabasebetaFinite Group Databasebeta| order | 10948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | D119⋊D23 |
| unambiguous semidirect product | D161⋊D17 |
| unambiguous semidirect product | D391⋊D7 |
| Fitting, socle, derived, Hall | C7×C17×C23 ⋊ C22 |
| Hall | C17×C23 ⋊ C2×D7 |
| Hall | C7×C23 ⋊ C2×D17 |
| Hall | C7×C17 ⋊ C2×D23 |
| Sylow | C23 ⋊ D7×D17 |
| Sylow | C17 ⋊ D7×D23 |
| Sylow | C7 ⋊ D17×D23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C17×C23 | C22 |
| LCS | G ▷ C7×C17×C23 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,7,17,23|d^a=d^16,e^a=e^22,c^b=c^6,d^b=d^16721 conjugacy classes — view the full character table.
| maximal subgroup of | (C17⋊AGL(1,𝔽7))⋊D23, C3×D119⋊D23, D391⋊D21, … |
| maximal normal subgroup of | (C17⋊AGL(1,𝔽7))⋊D23, C3×D119⋊D23 |
| maximal quotient of | C3×D119⋊D23, D391⋊D21, D161⋊D51, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10948, 20);